Question

Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.
y = -3x + 5
2y = -6x + 10
__

Answer 1

To determine the relationship between the two given equations by inspection, let's analyze them:

1. The first equation is:
\[
y = -3x + 5
\]

2. The second equation is given as:
\[
2y = -6x + 10
\]
We can simplify this equation by dividing everything by 2:
\[
y = -3x + 5
\]

Now we can see that both equations are identical:
\[
y = -3x + 5
\]
This means any solution that satisfies one equation will satisfy the other one as well.

Since both equations represent the same line, there are infinitely many solutions (every point on the line is a solution).

Thus, the answer is:
**3** for infinitely many solutions.